Having a relevant and well-polished portfolio can push you to the top of the heap in the interview process. It may help to make you memorable to the interviewer (for good reason rather than because you were annoying or ill-prepared as many applicants can be)
Of course, a portfolio alone will not land you the job, but having a well-developed portfolio with examples of work product that you are capable of creating with limited instruction/supervision will speak volumes about you that your resume may not.
When you bring your portfolio to an interview, it may be best to hold it for the end of the interview rather than letting it be a distraction too early when you want to be able to create a strong first impression. As good time to bring it out is when you are asked the question, “Is there anything else you would like us to know about you?”
You can respond (humbly, of course), “Well, I did bring some samples of my work. Here is my portfolio.” I would offer to leave them an electronic copy of the documents in the portfolio. Don’t leave the original. You should invest in having great presentation for the hard copy original of your portfolio, and it would be too expensive to leave every potential employer an original, but do allow them to go through it, and be ready to discuss the work that you have produced.
Interviewers love portfolios! It gives them something more on which to base their evaluation of you and recommendation to hire you. Of course, the caveat is that you should only include work you did and are capable of doing.